Reviews: Deep Learning without Poor Local Minima

The paper makes a significant dent in the central mystery of deep learning: why are neural networks so easy to optimize? The precision of the linear result is quite impressive! The nonlinear result still makes a implausible assumption, but is stronger than previous work and the implausibility is carefully discussed. The paper itself was a delight to read, though I will admit that the full proofs were a bit of a slog. My main question is whether the proofs could be simplified.